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Long title:

Statistical Downscaling of General Circulation Model

Outputs to Precipitation

Part 1: Calibration and Validation

Short title:

Downscaling of GCM Outputs to Precipitation

Calibration and Validation

D.A. Sachindraa*, F. Huanga, A. Bartona,b, and B.J.C. Pereraa

aVictoria University, P.O. Box 14428, Melbourne, Victoria 8001, Australia.

bUniversity of Ballarat, PO Box 663, Ballarat, Victoria 3353, Australia.

*Correspondence to: D. A. Sachindra, College of Engineering and Science, Footscray Park Campus, Victoria

University, P.O. Box 14428, Melbourne, Victoria 8001, Australia. E-mail:

sachindra.dhanapalaarachchige@live.vu.edu.au. Telephone: +61 03 9919 4907.

The authors acknowledge the financial assistance provided by the Australian Research Council Linkage Grant

scheme and the Grampians Wimmera Mallee Water Corporation for this project.

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Abstract

This paper is the first of two companion papers providing details of the development of two separate

models for statistically downscaling monthly precipitation. The first model was developed with

NCEP/NCAR reanalysis outputs and the second model was built using the outputs of Hadley Centre

Coupled Model version 3 GCM (HadCM3). Both models were based on the multi-linear regression

(MLR) technique and were built for a precipitation station located in Victoria, Australia. Probable

predictors were selected based on the past literature and hydrology. Potential predictors were selected for

each calendar month separately from the NCEP/NCAR reanalysis data, considering the correlations that

they maintained with observed precipitation. Based on the strength of the correlations, these potential

predictors were introduced to the downscaling model until its performance in validation, in terms of

Nash-Sutcliffe Efficiency (NSE), was maximised. In this manner, for each calendar month, the final sets

of potential predictors and the best downscaling models with NCEP/NCAR reanalysis data were

identified. The HadCM3 20th century climate experiment data corresponding to these final sets of

potential predictors were used to calibrate and validate the second model. In calibration and validation,

the model developed with NCEP/NCAR reanalysis data displayed NSEs of 0.74 and 0.70, respectively.

The model built with HadCM3 outputs showed NSEs of 0.44 and 0.17 during the calibration and

validation periods, respectively. Both models tended to under-predict high precipitation values and over-

predict near-zero precipitation values, during both calibration and validation. However, this prediction

characteristic was more pronounced by the model developed with HadCM3 outputs. A graphical

comparison of observed precipitation, the precipitation reproduced by the two downscaling models and

the raw precipitation output of HadCM3, showed that there is large bias in the precipitation output of

HadCM3. This indicated the need of a bias-correction, which is detailed in the second companion paper.

Keywords: Statistical downscaling, Precipitation, General Circulation Model

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1. INTRODUCTION

Changes in the global climate since the 20th century (notably rises in the global temperature), were mostly

attributed to anthropogenic greenhouse gas (GHG) emissions, rather than natural variability in climate

(Crowley, 2000). Furthermore, as stated in IPCC (2007), the rise in global and continental temperatures

during the 20th century can be credibly reproduced with climate models, only if both natural and

anthropogenic forces were considered. Sea level rise, reduction of snow coverage, extreme precipitation

events, heat waves and rise in the frequencies of hot events and tropical cyclones are considered to be

some of the impacts of climate change (Alavian et al., 2009).

Over the period 1997-2008, the average precipitation over the southern part of southeast Australia

declined by about 11% from the long term average, leading to a reduction in runoff of approximately 35%

(Chiew et al., 2010). The Australian state of Victoria suffered a severe drought (referred to as “the

Millennium drought”) from 1997, until the torrential rainfalls in late 2010 and early 2011. During 1998-

2007, annual average precipitation in Victoria decreased by about 13% from the long term average and

the highest decline in rainfall of 28%, occurred over the autumn months. The average rainfall in autumn

and early winter dropped well below the long term average, while the rainfall in summer remained as it

was (Timbal and Jones, 2008). This drought forced the introduction of severe water restrictions in many

regions of Victoria. The region southwest of Western Australia is experiencing a drought which has been

in effect since late 1960s (Smith et al., 2000). Unlike the Millennium drought, which has now ended, the

drought in southwest of Western Australia has not shown any signs of ending and is considered to have

experienced a step change in climate (Government of Western Australia Department of Water, 2009). The

changes in the climate described in the above examples are believed to be the possible impacts of

anthropogenic climate change and natural variability of the climate.

Precipitation is regarded as the predominant factor in determining the availability of water resources in a

catchment. The food supply of humans and animals, irrigation, hydropower generation and recreational

purposes are just some of the major sectors directly under the influence of precipitation. Hence it is

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understood that the reliable prediction of future precipitation, especially under a changing climate, is of

great importance in assessing future water availability.

General circulation models (GCMs) are considered the most reliable tools in studying climate change

(Maraun et al., 2010). They have proven their potential in reproducing the past observed climatic changes,

considering the GHG concentrations in the atmosphere (Goyal et al., 2011). However, GCMs produce

their projections at relatively coarse spatial scales and they are unable to resolve sub-grid scale features

such as topography, clouds and land use. Since GCMs generate outputs at coarse grid scales in the order

of a few hundred kilometres, their outputs cannot be directly used in catchment scale climate impact

studies, which usually need hydroclimatic data at fine spatial resolutions. The scale mismatch between the

GCM outputs and the hydroclimatic information needed at the catchment level is a major obstacle in

climate impact assessment studies of hydrology and water resources (Willems and Vrac, 2011).

As a solution to the scale mismatch between the GCMs outputs and the hydroclimatic information

required at catchment scale, downscaling techniques have been developed. Downscaling techniques are

classified into two broad classes; dynamic downscaling and statistical downscaling. In dynamic

downscaling, outputs of GCMs are fed into regional climate models (RCMs) as boundary conditions to

enable the prediction of the regional climate at the spatial scale of 5-50 kilometres (Yang et al., 2012).

This procedure is based on the complex physics of atmospheric processes and involves high

computational costs. In dynamic downscaling techniques, it is assumed that the parameterisation schemes

selected for the past climate are also valid for the climate in future. In addition, dynamic downscaling

techniques are highly dependant on the boundary conditions provided by the GCMs. However, dynamic

downscaling could produce spatially distributed hydroclimatic predictions over the catchment of interest

(Maurer et al., 2008).

Statistical downscaling relies on the empirical relationships derived between the GCM outputs (predictors

of downscaling models) and the catchment scale hydroclimatic variables (predictands of downscaling

models) such as precipitation, streamflow, and evaporation (Hay and Clark, 2003). Unlike dynamic

downscaling, statistical downscaling does not involve complex atmospheric physics and hence is

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computationally less expensive (Sachindra et al., 2012). In statistical downscaling, for the establishment

of relationships between the GCM outputs and the catchment scale hydroclimatic variables, preferably

long records of observed hydroclimatic data are required (Sachindra et al., 2013). This is because a long

record of observations could possibly contain the full variability of the observed climate and hence allow

the downscaling models to better model the changes in the climate. However this can limit the effective

use of statistical downscaling in data scarce regions. Statistical downscaling techniques are based on the

major assumption that the relationships derived between the GCM outputs and the catchment scale

hydroclimatic variables for the past observed climate are equally valid for the future, under changing

climate (von Storch et al., 2000). Also similar to dynamic downscaling, statistical downscaling techniques

are highly dependent on the outputs of the GCMs which are used as inputs to the downscaling model.

Statistical downscaling techniques are grouped under three categories; weather classification, regression

models and weather generators (Wilby et al., 2004). In weather classification methods, large scale

weather patterns are grouped under a finite number of discrete states (Anandhi, 2010). Then the links

between the catchment scale weather at certain times and the large scale weather patterns are identified.

Hence, by considering the large scale weather patterns at any given time, the corresponding catchment

scale weather can be deduced. The method of meteorological analogues (Timbal et al., 2009, Charles et

al., 2013; Shao and Li, 2013) and recursive partitioning (Schnur and Lettenmaier, 1998) are examples for

the weather classification techniques. Regression techniques develop either linear or non-linear regression

equations between the GCM outputs and the catchment scale hydroclimatic variables. Regression based

downscaling methods are regarded as the most widely used statistical downscaling techniques (Nasseri et

al., 2013). This is mainly due to their simplicity and effectiveness. Chu et al. (2010) used Multi-Linear

Regression (MLR) for downscaling GCM outputs to daily mean temperature, pan evaporation and

precipitation. Tisseuil et al. (2010) used Artificial Neural Networks (ANN), Generalized Additive Models

(GAM), Generalized Linear Models (GLM), and Aggregated Boosted Trees (ABT) for downscaling

GCM outputs to daily streamflows. Gene Expression Programming (GEP) and MLR techniques were

employed by Hashmi et al. (2011) for downscaling GCM outputs to daily precipitation. The Least Square

Support Vector Machine Regression (LS-SVM-R) was used by Anandhi et al. (2012) and Sachindra et al.

(2013) for downscaling GCM outputs to daily relative humidity and monthly streamflows respectively.

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Model Output Statistics (MOS) is a statistical downscaling technique used in post-processing the outputs

of climate or weather models (Maraun et al., 2010), by relating them with catchment scale observation

using a linear regression technique (Marzban et al. 2006). This enables the reduction of systematic bias in

the predictions of the model. Weather generators produce weather data for the future by scaling their

parameters according to the corresponding changes characterised in the GCM outputs for the future.

These techniques possess the advantage of generating series of climatic data of any desired length of time

with similar statistical properties as observations used in the weather generator (Khalili et al., 2009). The

combination of Markov chains and two parameter Gamma distribution is an example of a weather

generator (Richardson, 1981), in which Markov chains are used to predict the occurrences of a climatic

variable and the Gamma distribution is used to determine the corresponding amounts. The applications of

weather generators in statistical downscaling are found in the studies of Semenov and Stratonovitch

(2010), Iizumi et al. (2012), Khazaei et al. (2013).

In general, any statistical downscaling model is calibrated and validated (developed) using the reanalysis

outputs (e.g. NCEP/NCAR) and observations, corresponding to the past climate. For producing the future

projections, outputs of a GCM pertaining to a certain GHG emission scenario are introduced to this

downscaling model. This procedure does not provide a smooth transition from the model development

phase (calibration and validation) to the future projection phase, as the former and latter steps are

performed with the outputs of two different sources which have different levels of accuracy. In other

words, the inputs used in the development phase and the future projection phase of a conventional

downscaling model are not homogeneous. As a solution to this issue, a downscaling model calibrated and

validated with GCM outputs can be used in producing future projections with the outputs of the same

GCM, pertaining to a future GHG emission scenario. Since the outputs of the same GCM are used for the

model development and future projections, there is homogeneity in the modelling process. However, in

the published literature there was no evidence of past studies which attempted the use of a downscaling

model developed with GCM outputs.

This paper, which is the first of a series of two companion papers, discusses the calibration and validation

of two statistical downscaling models based on Multi-Linear Regression (MLR) technique. The two

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statistical downscaling models were developed separately, for downscaling monthly outputs of (1)

National Centers for Environmental Prediction / National Center for Atmospheric Research

(NCEP/NCAR) reanalysis and (2) Hadley Centre Coupled Model version 3 GCM (HadCM3), to monthly

precipitation. As the case study, a precipitation station located within the Grampians water supply system

in north-western Victoria in Australia was selected. A performance comparison between two downscaling

models for the calibration and validation phases was also performed.

Downscaling GCM outputs to precipitation at monthly temporal scale does not permit capturing the

variations of precipitation within a month (e.g. wet and dry days, precipitation intensity and extremes of

precipitation). However, still monthly precipitation projections produced using downscaling models could

aid in the management of water resources which include operations such as water allocation for crops,

domestic and industrial needs, and also environmental flows, especially in the planning stage of a water

resources project.

The remainder of this paper was structured as follows. The study area and the data used in the study were

briefly described in Section 2, followed by the generic methodology in Section 3. Thereafter, in Section 4,

the application of this methodology to the precipitation station considered was provided along with a

discussion on the model results. A summary on the model development process and results, along with

the conclusions drawn from the study were provided in Section 5. In the second paper the bias-correction

and future precipitation projections are detailed.

2. STUDY AREA AND DATA

The Grampians water supply system in north-western Victoria is a large multi reservoir system owned

and operated by the Grampians Wimmera Mallee Water Cooperation (GWMWater)

(www.gwmwater.org.au). For this study, a precipitation station at Halls Gap post office (Lat. -37.14˚,

Lon. 142.52˚, elevation from mean sea level about 236m), located in the Grampians system was selected.

At this station, the annual average precipitation over the period 1950-2010 was about 950mm. In this

region, winter and summer are the wettest and the driest seasons respectively. Observed daily

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precipitation record from 1950 to 2010 was obtained from the SILO database

(http://www.longpaddock.qld.gov.au/silo/) of Queensland Climate Change Centre of Excellence and

aggregated to monthly precipitation, for the calibration and validation of downscaling models. In that

observed daily precipitation record 31.2% of the data were missing and those missing data were filled by

the Queensland Climate Change Centre of Excellence in the SILO database using the spatial interpolation

method detailed in Jeffrey et al. (2001). In order to provide the inputs for the calibration and validation of

the first downscaling model, NCEP/NCAR monthly reanalysis data for the period 1950-2010 were

downloaded from http://www.esrl.noaa.gov/psd/. Monthly precipitation outputs produced by the HadCM

3 GCM for the 20th century climate experiment were extracted from the Programme for Climate Model

Diagnosis and Inter-comparison (PCMDI) (https://esgcet.llnl.gov:8443/index.jsp) for the period 1950-

1999, for developing the second downscaling model.

3. GENERIC METHODOLOGY

The first step of the downscaling exercise was to define an adequately large atmospheric domain above

the precipitation station. It was considered that an adequately large atmospheric domain would enable

sufficient atmospheric influence on the climate at the points of interest (e.g. a precipitation station) within

the catchment.

A set of probable predictor variables was identified based on a review of past literature on downscaling

GCM outputs to precipitation and hydrology. These probable variables are the most likely candidates to

influence precipitation at the catchment scale. In selecting predictors in the past studies (e.g. Timbal et al.

(2009), Anandhi (2008), Kannan and Ghosh (2013)), factors such as (1) availability in GCM and

reanalysis data sets, (2) reliable simulation by GCMs (3) usage in similar studies, (4) fundamentals of

hydrology, (4) correlations with the predictand etc were considered. Potential predictors are subsets of the

set of probable predictor variables. These sets of potential predictors are the most influential variables on

precipitation at the stations considered. The predictor-predictand relationships vary from season to season

and also from (geographic) region to region, following the spatio-temporal variations of the atmospheric

circulations (Karl et al., 1990). Therefore the sets of potential predictors also vary spatio-temporally. In

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this study, in order to better model the precipitation, considering the seasonal variations of the

atmospheric circulations, potential predictors were identified for each calendar month, and downscaling

models were developed separately for each of the 12 calendar months. Sachindra et al. (2013) found that

both Least Square SVM (a complex non-linear downscaling technique) and MLR (a relatively simple

linear downscaling technique) have comparable capabilities in directly downscaling GCM outputs to

catchment scale streamflows. Hence, in this study MLR technique was used to downscale GCM outputs

to catchment scale precipitation.

Following the methodology proposed by Sachindra et al. (2013), the probable predictors obtained from a

reanalysis database were split into 20 year time slices, in the chronological order. The Pearson correlation

coefficients (Pearson, 1895) between these probable predictors and the observed monthly precipitation

were calculated for each 20 year time slice and the whole period, at all grid points in the atmospheric

domain, for each calendar month. Thereafter, the probable variables which exhibited the best statistically

significant correlations (at 95 % confidence level, p = 0.05) with observed precipitation, over all 20 year

time slices and the whole period consistently, were extracted as the potential predictors. The consistently

correlated variables refer to the predictors which maintained correlations without any sign variations (e.g.

positive to negative or vice versa) and large variation in magnitudes over the time slices and the whole

period of the study. Once the selection of potential predictors was completed, two downscaling models

were developed (calibrated/validated) separately, the first using the reanalysis outputs and the second

with the corresponding 20th century climate experiment outputs of the GCM. The development of two

separate downscaling models, one with reanalysis outputs and the other with GCM outputs, enabled the

determination of how accurately the model developed with GCM outputs could reproduce the past

precipitation observations, in comparison to its counterpart model. Furthermore, this process allows for

understanding the potential of the downscaling model developed with GCM outputs, for its use in

producing the precipitation projections into future. Reanalysis data are accepted to be more accurate than

GCM outputs, owing to the rigorous quality control and corrective measures to which they are subjected

to (e.g. NCEP/NCAR reanalysis - Kalnay et al., 1996). Since the reanalysis outputs are more accurate

than the GCM outputs, the downscaling model built with reanalysis outputs should better perform in the

calibration and validation periods. If the downscaling model developed with GCM outputs was capable of

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reproducing the past precipitation observations adequately, it enables the use of this same model for the

future projections of precipitation. In this case, a homogeneous set of data produced by the same GCM is

used for the calibration, validation and future projection. Therefore, this can be regarded as a better

option, than using the GCM outputs pertaining to future on the downscaling model developed with

reanalysis outputs to project the precipitation at the station of interest into future.

For the calibration phase of the downscaling model developed with reanalysis data, the first two thirds of

these reanalysis (corresponding to potential predictors) and observed precipitation data (predictand) were

used, while the rest of the data were used for the model validation. The potential predictors for both

calibration and validation were standardised with the means and the standard deviations of reanalysis data

corresponding to the calibration phase (Sachindra et al., 2013). In model calibration, initially, the three

potential predictors which have shown the best correlations with precipitation over the whole period of

the study were introduced to the downscaling model. The parameters (coefficients and constants in the

MLR equations) of the downscaling model were optimised in calibration, by minimising the sum of the

squares of the errors. Then the model validation was performed with the calibrated model. The

performance of the model during calibration and validation in reproducing the observed precipitation was

assessed using the Nash-Sutcliffe efficiency (NSE) (Nash and Sutcliffe, 1970). Thereafter, the next

potential predictors which showed the best correlation with precipitation were introduced to the

previously added predictors of the downscaling model, one at a time. This process of stepwise addition of

potential predictors was practised until the model performance in terms of NSE in validation reaches a

maximum. This process allowed finding the best set of potential predictors and the best downscaling

model for a calendar month. The downscaling model calibration and validation were performed for each

calendar month separately.

If the stepwise development was not employed in the development of the model based on the reanalysis

outputs, all potential predictors could have been introduced into the downscaling model at once. This

could have introduced data redundancy errors due to the inter-dependency or cross-correlations between

the predictors leading, to over-fitting in calibration and under-fitting in validation. The stepwise model

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development and selection of the model which showed the best performance in validation guaranteed the

avoidance of selection of models which showed over-fitting in calibration and under-fitting in validation.

As mentioned earlier in this paper, the second downscaling model (with sub-models for each calendar

month) was developed (calibrated/validated) with the GCM outputs corresponding to the climate of the

20th century. In the calibration and validation of this downscaling model, observed precipitation at the

station of interest was used as the predictand. The same calibration period used for first model was also

used for this model. The rest of the GCM data were used for the validation. Inputs for both the calibration

and validation phases of this model were standardised with the means and the standard deviations of the

GCM outputs pertaining to the calibration period. The best potential predictors identified in the

calibration and validation processes of the downscaling model developed with reanalysis outputs were

also used in the development of this model, assuming the validity of these potential predictors for both

downscaling models. The calibration of the second model was performed for each calendar month by

introducing the 20th century climate outputs of the GCM pertaining to the best potential predictors. The

optimum parameters of the MLR based downscaling models were determined by minimising the sum of

the squared errors between the model predicted precipitation and the observed precipitation. These MLR

models with the same parameters determined in the calibration phase were used in the validation. Unlike

in the development of the model which was driven with reanalysis outputs, stepwise development process

was not adopted in building the model driven with GCM outputs, as the best potential variables were

already identified.

Graphical and numerical comparisons between the observed precipitation and precipitation outputs of the

above described two statistical downscaling models were performed. Both graphical and numerical

assessments were employed, as numerical assessments alone may not be robust enough in the evaluation

of model performances. The graphical comparison of precipitation included the time series and scatter

plots of the model reproduced precipitation against observations. The numerical assessment of the two

downscaling models was done by statistical measures such as average, standard deviation, coefficient of

variation, NSE, Seasonally Adjusted NSE (SANS) (Wang, 2006; Sachindra et al., 2013) and the

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coefficient of determination (R2). Note that all MLR based downscaling models discussed in this paper

were developed using the statistics toolbox in MATLAB (Version - R2008b).

4. APPLICATION

The generic methodology described in Section 3 was applied to the precipitation station at the Halls Gap

post office in the operational area of GWMWater, Victoria, Australia.

4.1. Atmospheric domain for downscaling

There are no clear guidelines on the selection of the optimum size of the atmospheric domain for a

statistical downscaling study. Najafi et al. (2011) successfully used an atmospheric domain with 7 X 4

grid points in the longitudinal and latitudinal directions respectively at a spatial resolution of 2.5˚ in both

directions, for the statistical downscaling of outputs of CGCM3 to monthly precipitation. Their study

demonstrated that the atmospheric domain does not necessarily have to be a square in shape. However, if

the atmospheric domain is too rectangular in shape, the influences of large scale atmospheric circulations

on the point of interest in the catchment are more considered on the wider sides of the domain, and the

influences coming from the narrower sides are less considered or neglected. Hence, such domain shape

should be avoided in statistical downscaling. A larger atmospheric domain increases the computational

cost and time involved in the investigation. However, a larger domain aids in identifying influences of

large scale atmospheric circulations over a wider area. When the atmospheric domain is too small, it may

not be able to adequately capture the atmospheric circulations responsible for the hydroclimatology in the

catchment. Therefore, the atmospheric domain which is an important component of any statistical

downscaling study should be of adequate size and of an appropriate shape. In general a domain size of 6

X 6 grid points at a spatial resolution of 2.5˚ in both longitudinal and latitudinal directions is a regarded as

an adequate size (Tripathi et al., 2006). An atmospheric domain with spatial dimensions of 7 X 6 grid

points at a spatial resolution of 2.5˚ in both longitudinal and latitudinal directions was selected for the

downscaling study described in this paper. The size of this atmospheric domain was determined

considering its ability to represent the large scale atmospheric phenomena which influence the

precipitation at the point of interest and also the computational cost. The same atmospheric domain over

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the same study area was successfully used by Sachindra et al. (2013) for statistically downscaling GCM

outputs to catchment streamflows. The spatial resolution of this atmospheric domain was maintained at

2.5˚ in both longitudinal and latitudinal directions, making it compliant with the spatial resolution of the

NCEP/NCAR reanalysis outputs. The atmospheric domain used in this study is shown in Figure 1. The

shaded region in Figure 1 depicts the operational area of GWMWater, and the precipitation station

considered in this study is located in its southmost region.

Figure 1 Atmospheric domain for downscaling

4.2. Selection of probable and potential predictors for downscaling

A pool of probable predictors was selected based on hydrology and past studies by Anandhi et al. (2008)

and Timbal et al. (2009), on downscaling GCM outputs to precipitation. In the downscaling study by

Timbal et al. (2009), predictor variables influential on the generation of precipitation, over the south and

south eastern Australia (this includes the present study area) were identified. The probable predictor pool

selected for the study described in this paper consisted of geopotential heights at 200hPa, 500hPa,

700hPa, 850hPa and 1000hPa pressure levels; relative humidity at 500hPa, 700hPa, 850hPa and 1000hPa

pressure levels; specific humidity at 2m height, 500hPa, 850hPa and 1000hPa pressure levels; air

temperatures at 2m height, 500hPa, 850hPa and 1000hPa pressure levels; surface skin temperature,

surface pressure, mean sea level pressure, surface precipitation rate, and zonal and meridional wind

speeds at 850hpa pressure level. These probable predictors were common for all calendar months. The

monthly data for these 23 probable predictors for the 42 grid points shown in Figure 1 were extracted

from the NCEP/NCAR reanalysis data archive at http://www.esrl.noaa.gov/psd/.

The probable predictors and the observed monthly precipitation totals from 1950 to 2010 were split into

three 20 year time slices; 1950-1969, 1970-1989, and 1990-2010. The last time slice was 21 years in

length. The Pearson correlation coefficients between the probable predictors and the observed monthly

precipitation were calculated for all three time slices and the whole period (1950-2010), at each grid point

in the atmospheric domain (see Figure 1). The probable predictors which showed good statistically

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significant correlations (at 95 % confidence level, p = 0.05) consistently over the three time slices and the

whole period were selected as the potential predictors (Sachindra et al., 2013). This process was repeated

for all 12 calendar months, yielding 12 sets of potential predictors.

The El Niño - Southern Oscillation (ENSO) and the Indian Ocean Dipole (IOD) are regarded as two large

scale atmospheric phenomena influential on the climate of Victoria, Australia. A correlation analysis

performed over the period 1950-2010 between the Southern Oscillation Index (SOI) which is

representative of ENSO and observed precipitation at the Halls Gap post office indicated that these

correlations vary between 0.03 (March) and 0.33 (October). Similarly, the correlations between the

Dipole Mode Index (DMI) which is representative of IOD and observed precipitation ranged between -

0.01 (February) and -0.46 (August) during the period 1958-2010. Hence, it was realised that the

influences of these large scale atmospheric phenomena on the observed precipitation at the Halls Gap post

office are weak in nature. Therefore it was understood that the inclusion of such indices in the inputs to

the downscaling models will not lead to any improvement to the precipitation predictions. Furthermore,

Chiew et al. (1998) detailed the influences of ENSO on the rainfall, drought and streamflows in Australia,

using the SOI and Sea Surface Temperature (SST), and concluded that, the correlations between these

ENSO indicators and hydroclimatic variables are not sufficiently strong for a consistent prediction.

4.3. MLR downscaling model calibration and validation

4.3.1 Model calibration and validation with NCEP/NCAR data

The potential predictors selected from the probable pool were separated into two chronological groups;

1950 to 1989 and 1990 to 2010, the former for model calibration and the latter for model validation. The

potential predictors were standardised for both calibration and validation periods using the means and the

standard deviations pertaining to the period 1950 to 1989 (calibration period). The standardised potential

variables were ranked based on the magnitude of their correlations with the observed monthly

precipitation, over the whole period of the study (1950-2010). Then these potential variables were

introduced to the MLR based downscaling model as described in Section 3. In the manner described in

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Section 3, for each calendar month the best set of potential predictors and the best MLR based

downscaling model were selected. Table 1 shows the final (or the best) set of potential predictors used in

the downscaling model developed with NCEP/NCAR reanalysis outputs for the month of January. Also

this table contains the correlations between the observed precipitation and the final set of potential

predictors, during the three 20 year time slices and the whole period of the study.

Table 1 Final set of potential predictors used in the January downscaling model and their correlations

with observed precipitation in each time slice and whole period.

Table 2 provides the final sets of potential predictors used in the downscaling models in each calendar

month. The final sets of potential predictors used in the downscaling models consisted of: surface

precipitation rate; specific humidity, relative humidity and geopotential heights at various pressure levels;

mean sea-level pressure; surface pressure; and zonal and meridional wind speeds at 850hPa pressure

level. However, surface precipitation rate was identified as the most influential potential predictor on

precipitation, appearing in the final sets of potential predictors for all calendar months except July.

Surface precipitation rate produced by GCMs is a precipitation flux (precipitation per unit time across

unit area at earth surface) which is analogous to precipitation at a point over a specific time period (e.g.

daily or monthly precipitation). Therefore the strong influence of surface precipitation rate on monthly

precipitation was justified. The highest correlations between the NCEP/NCAR precipitation rate and the

observed precipitation over the period 1950-2010 within each calendar month were; June (0.82), August

(0.82), October (0.79), September (0.77), December (0.74), May (0.71), January (0.69), April (0.64),

February (0.61), March (0.61) and November (0.48). Precipitation outputs of GCMs have been also used

in the past downscaling studies. Timbal et al. (2009) used precipitation rate in downscaling daily

precipitation and Tisseuil et al. (2010) used precipitation rate for downscaling daily streamflows. Maraun

et al. (2013) stated that despite the errors, the precipitation output of a GCM can still contain useful

information about the observed precipitation. Hence it was realised that precipitation output of a GCM

can be used as an input to a downscaling model.

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Specific humidity (mass of water vapour per unit mass of air), and relative humidity (ratio of actual water

vapour pressure of the air to the saturation vapour pressure) at various pressure levels are indicators of the

atmospheric water vapour content which leads to the formation of clouds (Peixoto and Oort, 1996).

Humidity variables (relative or specific humidity) which are indictors of the atmospheric water vapour

content were potential predictors in 7 (February, March, May, September, October, November and

December) of the 12 calendar months. According to Nazemosadat and Cordery (1997), geopotential

heights are influential on the generation of precipitation, as they are representative of large scale

atmospheric pressure variations such as the El Niño Southern Oscillation (ENSO). Zonal and meridional

wind fields are influential on the evaporation from open surface water bodies and they govern the

movement of rain bearing clouds (Bureau of Meteorology, 2010), and hence it was suitable to include

wind fields in the final sets of potential predictors. It is noteworthy to mention that, according to Table 2,

except in August and November, grid point {4,4} found to be a dominant location for the final sets of

potential predictors. The grid point {4,4} is the closest grid point to the precipitation station considered in

this study.

In general, humidity variables and precipitation rate are more capable of explaining the precipitation

process (refer to Table 2). However as shown in Table 2, in the month of July, the set of potential

predictors used in the downscaling models contained only the wind speeds and the geopotential heights at

850hPa. It was realised that these variables are still able to explain the precipitation process with a good

degree of accuracy, as the downscaling model developed for July using the NCEP/NCAR reanalysis

outputs displayed NSEs of 0.58 and 0.50 in the calibration and validation phases respectively.

Furthermore, as these potential variables are selected based on the magnitude and also the consistency of

correlations with observed precipitation over time, it is argued that the final sets of potential predictors

used in the downscaling models are able to characterise the changes in precipitation at the point of

interest, also in the future.

Table 2 Final sets of potential predictors for each calendar month

17

In Table 2, it could be found that the majority of the potential predictors in the final sets were selected

from the grid points surrounding the precipitation station of interest [(3,3), (3,4), (3,5), (4,3), (4,4), (4,5),

(5,3), (5,4) and (5,5)]. However some potential predictors in the final sets were selected from the distant

grid points of the domain as the precipitation at the station of interest is not only influenced by the

atmosphere in close proximity to the station but also by the atmospheric processes that occur far away.

The best grid locations of the potential predictors provided in Table 2 were selected not only based on the

strength of the correlation between the potential predictors and observed precipitation, but also

considering the consistency of the correlation over three time slices and the whole period of the study.

Therefore it was assumed that the best grid locations of the final sets of potential predictors used in this

study will remain the same in future.

4.3.2 Model calibration and validation with HadCM3 20th century climate experiment data

The 20th century climate experiment data of HadCM3 GCM were obtained for the period 1950-1999,

corresponding to the final sets of potential predictors shown in Table 2. HadCM3 model has been forced

with both natural and anthropogenic forcings to reproduce the climate of the 20th century (Knight, 2003).

As the natural forcings; sea-surface temperature (SST) and sea-ice anomalies, variations in the total solar

irradiance and stratospheric volcanic aerosols etc have been used in HadCM3. As anthropogenic forcings;

GHG concentrations in the atmosphere, changes in tropospheric and stratospheric ozone, the effects of

atmospheric sulphate aerosols and changes in land surface characteristics have been used in HadCM3.

The 20th century climate experiment data of HadCM3 were split into two groups; (a) 1950-1989 for

model calibration and (b) 1990-1999 for the model validation. HadCM3 data for both the calibration and

validation phases were standardised with the means and the standard deviations of HadCM3 data

corresponding to 1950-1989 period. In calibration, the standardised sets of data pertaining to the best

potential predictors shown in Table 2 were introduced to the MLR based downscaling model. During

calibration, the optimum values for the model parameters were determined by minimising the sum of

squared errors between the model predicted and observed precipitation values. In validation, the HadCM3

data for the 1990-1999 period were introduced to the calibrated MLR models. The same procedure was

repeated for all calendar months. Unlike in the calibration and validation of the downscaling model which

18

was developed with NCEP/NCAR reanalysis outputs, the stepwise development procedure was not

adopted in these models. A correlation coefficient analysis performed between the 20th century climate

experiment outputs of HadCM3 and NCEP/NCAR reanalysis outputs over the period 1950-1999,

revealed that these correlations are quite weak (e.g. 0.2 – 0.4). Hence it was realised that HadCM3

outputs pertaining to the 20th century climate experiment contain large bias. Therefore it was understood

that whether the final sets of potential predictors are selected using a stepwise procedure or not, they will

not change the performance of the model developed with HadCM3 outputs. It was assumed that final sets

of potential predictors identified in the development of the model driven with NCEP/NCAR outputs are

also applicable for this model. The difference between the statistical downscaling models built with the

HadCM3 20th century experiment data (Model(HadCM3)) and the models built with the NCEP/NCAR

reanalysis data (Model(NCEP/NCAR)) was that these two models had different optimum values for their

parameters (coefficients and constants in MLR equations).

4.3.3 Calibration and validation results of the downscaling models

Figure 2 shows the time series of monthly observed precipitation and monthly precipitation reproduced

by the downscaling model developed with NCEP/NCAR data, for the period 1950-2010. According to

Figure 2, the monthly precipitation reproduced by this downscaling model, was in close agreement with

the observed precipitation during both calibration and validation periods. Although the model validation

was performed in a relatively dry period which included the Millennium drought (1997-2010), this

downscaling model has been able to capture the monthly precipitation pattern and the magnitude with

good accuracy.

Figure 2 Observed and Model (NCEP/NCAR) reproduced monthly precipitation (1950 to 2010)

Figure 3 shows the scatter plots of monthly observed precipitation and precipitation reproduced by the

downscaling model developed with NCEP/NCAR data, for the calibration (1950-1989) and validation

(1990-2010) phases. As seen in Figure 3, during both the calibration and validation periods, near zero

monthly precipitation values were over predicted and relatively large precipitation values were under

19

predicted. However, these scatter plots of the model predictions against the observations further

confirmed that, the prediction capabilities of the model developed with NCEP/NCAR data in validation

are very much comparable with those during calibration.

Figure 3 Scatter plots of observed and Model (NCEP/NCAR) reproduced monthly precipitation for calibration

(1950-1989) and validation (1990-2010)

Figure 4 illustrates the time series of monthly observed precipitation and monthly precipitation

reproduced by the downscaling model built with HadCM3 data, for the period 1950-1999. It was seen that

this model was not able to satisfactorily reproduce the high precipitation values. Furthermore, the

agreement between the observed and model reproduced precipitation was much less compared to that of

the model developed with NCEP/NCAR reanalysis outputs. However the model developed with HadCM3

outputs properly captured the pattern of the observed precipitation as shown in Figure 4. It should be

noted that the validation phase of the model developed with HadCM3 data was confined to the period

1990-1999, due to the unavailability of data beyond year 1999, under the 20th century climate experiment.

Figure 4 Observed and Model (HadCM3) reproduced monthly precipitation (1950 to 1999)

Figure 5 represents the scatter plots for the calibration (1950-1989) and validation (1990-1999) phases of

the downscaling model developed with HadCM3 data. It was seen that in the calibration and validation

phases, high precipitation values were largely under-predicted. During both phases, the model displayed a

clear trend of over-predicting the majority of low precipitation values. However, these characteristics

were also seen in the predictions of the model developed with NCER/NCAR data, but with less intensity.

Statistical downscaling models in general fail to capture the full range of the variance of a predictand such

as precipitation (Wilby et al., 2004). This is because, in general the variance in the observations of

precipitation is much greater than the variance in the large scale atmospheric variables obtained from the

GCM or the reanalysis data. When the downscaling model is run with the GCM or the reanalysis data it

tends to explain the mid range of the variance of the observed precipitation better than the low and high

20

extremes. Therefore statistical downscaling models in general tend to reproduce the average of the

precipitation better than the low and high extremes. In other words, this results in an under-estimation of

large precipitation values and over-estimations of near zero precipitation values. Tripathi et al. (2006)

also commented that even a downscaling model based on support vector machine technique (complex

non-linear regression technique) fails to properly reproduce the extremes of precipitation though it

captures the average well.

Figure 5 Scatter plots of observed and Model (HadCM3) reproduced monthly precipitation for calibration

(1950-1989) and validation (1990-1999)

The performances of the two downscaling models, during the calibration and validation phases were

numerically assessed by comparing the mean, the standard deviation and the coefficient of variation of

the model predictions with those of observations, and these results are shown in Table 3. It can be seen

that both downscaling models developed with NCEP/NCAR and HadCM3 outputs reproduced the

observed averages of the precipitation with good accuracy, in both calibration and validation phases. This

finding was quite consistent with that of Sachindra et al. (2013), in which MLR and LS-SVM techniques

were employed for downscaling NCEP/NCAR outputs to streamflows. However, in the present study,

neither of the two models properly captured the standard deviation and the coefficient of variation of the

observed precipitation, during both the calibration and validation phases. This characteristic was more

noticeable in the outputs of the downscaling model developed with HadCM3 data. It indicated that, in

particular, the model developed with HadCM3 data could not reproduce the entire variance of the

observed precipitation. In Figure 4, the same characteristic was seen in the time series plots. This

characteristic was seen with less severity in the outputs of the model developed with NCEP/NCAR

reanalysis data.

Table 3 Performances of downscaling models in calibration and validation

The model performances in calibration and validation were further quantified with the NSE, the SANS

and the coefficient of determination (R2). The SANS considers the seasonal means of precipitation in

21

measuring the model performances, unlike the original NSE, which considers only the mean of

precipitation for the whole period. During calibration, the statistical downscaling model developed with

NCEP/NCAR reanalysis data displayed NSE, SANS and R2 of 0.74, 0.66 and 0.74 respectively. However

for the same period, the downscaling model developed with HadCM3 outputs, produced NSE, SANS and

R2 of 0.44, 0.26 and 0.44 respectively. In the validation phase, the model developed with NCEP/NCAR

outputs produced NSE, SANS and R2 of 0.70, 0.61 and 0.72. During the validation period, the model

developed with HadCM3 outputs, produced NSE, SANS and R2 of 0.17, -0.20 and 0.22 respectively.

These findings indicated that both downscaling models have performed relatively better during the

calibration period than in the validation period. However, it was seen that the downscaling model

developed with NCEP/NCAR data performed well in the calibration and validation phases, compared to

its counterpart model which was built with HadCM3 outputs. This statement was further supported by the

findings of scatter plots shown in Figures 3 and 5.

Figure 6 depicts the agreement between the precipitation reproduced by the model developed with

NCEP/NCAR outputs and the observed precipitation, during the calibration (1950-1989) and validation

(1990-2010) periods, on a seasonal basis. As shown in Figure 6, it was determined that this model

demonstrates good capabilities in reproducing the observations in calibration and validation, in all four

seasons, despite the tendencies of under-predicting high precipitation values and over-predicting near zero

precipitation values which were evident in all four seasons. The four seasons are defined as summer

(December-February), autumn (March-May), winter (June-August) and spring (September-November).

Figure 6 Seasonal scatter plots of observed and Model (NCEP/NCAR) reproduced monthly precipitation for

calibration (1950-1989) and validation (1990-2010)

Figure 7 displays the seasonal scatter plots for the calibration (1950-1989) and validation (1990-1999)

periods of the model developed with HadCM3 outputs. Large under-predictions of precipitation were

seen in all four seasons during both the calibration and validation phases of this model. During all four

seasons in the validation period, a relatively poor agreement between the observed and model reproduced

precipitation was seen. This characteristic was more intense in autumn, winter and spring than in summer.

22

Figure 7 Seasonal scatter plots of observed and Model (HadCM3) reproduced monthly precipitation for

calibration (1950-1989) and validation (1990-1999)

Table 4 shows the seasonal statistics of the observed precipitation and the precipitation reproduced by the

models developed with NCEP/NCAR reanalysis and HadCM3 data, for the calibration and validation

periods. In the calibration phase, during all four seasons, averages of the observed precipitation were near

perfectly reproduced by both downscaling models. In the validation phase, although not as good as in

calibration, both models were capable in reproducing the averages of observed precipitation in all four

seasons with some under and over-predictions. During all four seasons in the validation period, both

downscaling models tended to over-predict the average of the observed precipitation. This was due to the

fact that the calibration was performed over a wetter period and the validation was done during a

relatively dryer period. However, according to Figures 2 and 4 both downscaling models were able to

adequately capture the precipitation pattern seen in the observations, throughout the calibration and

validation periods. The under-estimation of the standard deviation and the coefficient of variation was

seen in all four seasons of both models, during the calibration and validation periods. This characteristic

was more severe in the case of the model developed with HadCM3 outputs. Since there is a large scale

gap between the GCM outputs and the catchment scale, not all the variance in observations of a

predictand (at a point in the catchment) can be explained by the GCM. Therefore, regression based

statistical downscaling techniques are capable of capturing only the part of the variance (deterministic

component of the variance) of a predictand which is conditioned by the GCM (Hewitson et al., 2013).

The local scale random variance of the predictand (stochastic component of the variance) is not simulated

by the regression based downscaling models, as it is not explicitly explained by the GCM. At the

catchment scale, capturing the full variance of a predictand is important. This can be achieved by the

application of a suitable bias-correction method for post processing the outputs of the downscaling model

(Maraun, 2013). Techniques such as randomization may also help in capturing the full variance of a

predictand (von Storch, 1999).

23

In the model developed with NCEP/NCAR data, the best performances in calibration in terms of NSE and

R2 were seen during winter while the lowest performances were observed in summer. For this model, in

validation, autumn produced the best performance. The model developed with HadCM3 outputs showed

relatively low NSE and R2 in all four seasons of the calibration period. The negative NSEs were seen in

autumn, winter and spring during the validation period, which indicated the limited performances of this

downscaling model.

As mentioned in Section 1, the largest drop in precipitation over Victoria during the Millennium drought

was observed in autumn. The decline in the average of the observed precipitation in autumn, during the

Millennium drought (1997-2010), at the station considered in this study, was 27.5%, from the long-term

average (1950-1989). The downscaling model developed with NCEP/NCAR reanalysis outputs was able

to successfully reproduce this large drop in the average as 22.4%.

Table 4 Seasonal performances of downscaling models

According to the findings discussed previously, it was realised that the downscaling model developed

with NCEP/NCAR reanalysis data has better potential in downscaling precipitation, in comparison with

its counterpart model built with HadCM3 outputs. This was due to the better quality of NCEP/NCAR

reanalysis outputs characterised by better synchronicity with observed precipitation, high precipitation

simulation etc in comparison to those of HadCM3 outputs. Furthermore, it was seen that MLR has the

potential for modelling the relationship between the predictors and the monthly precipitation adequately.

As shown in Tables 3 and 4, and Figure 3 with the final sets of potential variables given in Table 2, the

downscaling model developed with NCEP/NACR reanalysis outputs reproduced the observed

precipitation with good degree of accuracy. Therefore it was realised that the final sets of potential

variables used in the downscaling models are capable of capturing the precipitation process to a good

degree.

Figure 8 shows the exceedance probability curve for the observed precipitation, precipitation reproduced

by the downscaling models with NCEP/NCAR and HadCM3 outputs, and the raw precipitation output of

24

HadCM3 model for the 20th century climate experiment at grid point {4,4} (see Figure 1 for location),

over the period 1950-1999. Since point {4,4} is the closest grid point to the precipitation station,

HadCM3 20th century climate experiment outputs at this point was considered to be representative of the

precipitation station considered in this study. Note that the precipitation rate (which was the observed

precipitation equivalent output of HadCM3) was converted to monthly precipitation, for plotting the

corresponding exceedance curve in Figure 8.

Figure 8 Precipitation probability exceedance curves (1950 to 1999)

According to Figure 8 it was seen that there is a large mismatch between the raw precipitation output at

grid point {4,4} of HadCM3 model and the observed precipitation, during the period 1950-1999. The

large bias in the precipitation output of HadCM3 indicated that its regional precipitation simulation is less

reliable. Larger differences between the observations and raw HadCM3 precipitation outputs were seen

for precipitations with low probability of exceedance, such as extremely high precipitations. Furthermore,

relatively small anomalies were seen for precipitation values with low magnitudes. For the majority of

exceedance probabilities, this mismatch was seen as a large under-prediction in HadCM3 precipitation

outputs. The mismatch between the observations and the raw HadCM3 precipitation output was mainly

due to the bias present in HadCM3 outputs. As defined by Salvi et al. (2011), bias is the difference

between the GCM outputs and the pertaining observations. GCM bias is a result of the limited knowledge

of the atmospheric processes and the simplified representation of the complex climate system in GCMs

(Li et al., 2010). The other possible factor contributing to the poor agreement between observations and

HadCM3 outputs is, that grid point {4,4} may not exactly represent the precipitation at the station

considered in this study. Furthermore, in case of the precipitation gauge located at the Halls Gap post

office, topographical reasons also have possibly contributed to the bias in the GCM outputs, as Halls Gap

is located in a valley surrounded by a mountain range.

It was noted that the mismatch between the observations and the precipitation downscaled with HadCM3

outputs was less in comparison with that between the observations and the raw precipitation outputs of

HadCM3 at grid point {4,4}. This indicated that when the raw outputs of HadCM3 are statistically

25

downscaled to monthly precipitation, the impact of bias in these raw HadCM3 outputs, on downscaled

precipitation was less evident. However, this reduction in bias was not adequate as still there was

considerable mismatch between the observed and downscaled precipitation (refer to Figure 8). Therefore,

it could be argued that a correction to the bias that is present in HadCM3 outputs is needed in producing

precipitation projections into future. It was seen that the precipitation exceedance curve of raw

precipitation output of HadCM3 at grid point {4,4} had deviated largely from the precipitation

exceedance curve of observations. However, the exceedance curves of precipitation reproduced by the

downscaling models developed with NCEP/NCAR reanalysis outputs and HadCM3 outputs were in

relatively better agreement with the precipitation exceedance curve of observed precipitation. This led to

the conclusion that, the precipitation outputs of the downscaling models developed with NCEP/NCAR

reanalysis outputs and HadCM3 outputs are much better than the raw precipitation output of HadCM3 at

grid point {4,4}. Furthermore, considering the limited agreement seen between the precipitation

downscaled with the NCEP/NACR and HadCM3 outputs, it was realised that there is a quality mismatch

between the data of these two sources. The second paper of this series of two companion papers,

describes the bias correction and the precipitation projections produced into future in detail.

5. SUMMARY AND CONCLUSIONS

This paper, which is the first of a series of two companion papers, discussed the development (calibration

and validation) of two precipitation downscaling models, employing the multi-linear regression (MLR)

technique. The first statistical downscaling model was developed with the NCEP/NCAR reanalysis

outputs and the second downscaling model was developed with the HadCM3 outputs. The precipitation

station at the Halls Gap post office which is located in the north western part of Victoria, Australia was

selected for the demonstration of the development process of the two downscaling models.

It is the general practice to calibrate and validate the downscaling model with some form of reanalysis

data (e.g. NCEP/NCAR) for the past climate, and use the outputs of a GCM pertaining to future on the

same downscaling model for the projection of climate into future. The major disadvantage of this

26

procedure is that, for the model development and future projections, data from two entirely different

sources are used. This study investigated the potential of using a downscaling model calibrated and

validated with GCM outputs, which does not have the above issue.

The selection of probable predictors for these downscaling models was based on the past statistical

downscaling studies and hydrology. Potential predictors were extracted for each calendar month from the

set of probable predictors considering the Pearson correlations between the probable predictors and

observed precipitation, under three 20 year time slices (1950-1969, 1970-1989, and 1990-2010) and the

entire period of the study (1950-2010). Potential predictors obtained from the NCEP/NCAR reanalysis

outputs were introduced to the MLR based downscaling model, sequentially, based on the magnitude of

the correlation between observed precipitation and predictors, over the whole period of the study. This

process was continued until the model performances in validation in terms of NSE was maximised. In this

manner, the final sets of potential predictors for each calendar month were identified, and downscaling

models for each calendar month were developed separately. The HadCM3 outputs corresponding to the

final sets of potential predictors identified previously were used for the development of the second

downscaling model. It was assumed that these final sets of potential predictors are valid for both

downscaling models, developed with NCEP/NCAR and HadCM3 outputs.

The MLR based downscaling model developed with NCEP/NCAR reanalysis outputs proved capable in

reproducing the observed monthly precipitation during both calibration (1950-1989) and validation

(1990-2010) phases. The performances of this model in calibration were slightly better than those in

validation. This model was also able to capture the precipitation drop occurred during the Millennium

drought (1997-2010) satisfactorily. However, it displayed tendencies of over-predicting low precipitation

values and under-predicting high precipitation values during both the calibration and validation periods.

On the other hand, the MLR based downscaling model developed with HadCM3 outputs displayed

limited performances with respect to the model developed with NCEP/NCAR reanalysis outputs during

both calibration and validation stages. This model performed better during calibration (1950-1989) than

in validation (1990-1999). Similar to the model developed with NCEP/NCAR reanalysis outputs, this

27

downscaling model also displayed tendencies of over-predicting and under-predicting low and high

precipitation values respectively. However, the over and under-predictions associated with the model

developed with HadCM3 outputs were much severe than those for its counterpart downscaling model.

Due to the termination of HadCM3 outputs at 1999 for the 20th century climate experiment, the validation

phase of this downscaling model was confined to 1990-1999. Therefore it was not possible to see how

this downscaling model will reproduce the precipitation during the Millennium drought.

The conclusions drawn from this study are:

1) The precipitation rate which is the precipitation equivalent output of a GCM was found as the most

influential predictor on precipitation at the station of interest, over the entire year, except in July;

2) Humidity, geopotential heights, mean sea level and surface pressure, and wind speeds also showed

good correlations with observed precipitation consistently over time;

3) The downscaling model developed with NCEP/NCAR reanalysis outputs performed well in both

calibration and validation, while the performances of the model developed with HadCM3 outputs

were limited;

4) There was a quality mismatch between the NCEP/NCAR reanalysis and HadCM3 outputs, over the

period 1950-1999; and

5) A bias-correction should be applied in projecting the precipitation into future at the station of interest.

The application of the bias-correction and the projections of precipitation into future are presented in the

second companion paper of this series of papers.

28

ACKNOWLEDGEMENTS

The authors acknowledge the financial assistance provided by the Australian Research Council Linkage

Grant scheme and the Grampians Wimmera Mallee Water Corporation for this project. The authors also

wish to thank the editor and the two anonymous reviewers for their useful comments, which have

improved the quality of this paper.

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Tasmania

New South WalesSouth Australia

1350 137.50 1400 142.50 1450 147.50 1500

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Precipitationstation Victoria

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Figure 2 Observed and Model (NCEP/NCAR) reproduced monthly precipitation (1950 to 2010)

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Figure 3 Scatter plots of observed and Model (NCEP/NCAR) reproduced monthly precipitation for

calibration (1950-1989) and validation (1990-2010)

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Figure 4 Observed and Model (HadCM3) reproduced monthly precipitation (1950 to 1999)

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Figure 5 Scatter plots of observed and Model (HadCM3) reproduced monthly precipitation for calibration (1950-1989) and validation (1990-1999)

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NSE=0.63 / R2=0.63 NSE=0.75 / R2=0.71

NSE=0.70 / R2=0.70 NSE=0.58 / R2=0.63

NSE=0.67 / R2=0.67 NSE=0.64 / R2=0.65

(a) Calibration (b) Validation

Figure 6 Seasonal scatter plots of observed and Model (NCEP/NCAR) reproduced monthly precipitation for calibration (1950-1989) and validation (1990-2010)

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NSE=0.34 / R2=0.34 NSE= -0.58 / R2=0.04

NSE=0.17 / R2=0.17 NSE= -0.20/ R2=0.00

NSE=0.32 / R2=0.32 NSE= -0.15/ R2=0.09

(a) Calibration (b) Validation

Figure 7 Seasonal scatter plots of observed and Model (HadCM3) reproduced monthly precipitation for calibration (1950-1989) and validation (1990-1999)

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Observed precipitation 1950-1999

MLR reproduced precipitation with NCEP/NCAR outputs 1950-1999

MLR reproduced precipitation with HadCM3 outputs 1950-1999

20th Century raw precipitation output of HadCM3 at point {4,4} 1950-1999

Exceedance probability

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Figure 8 Precipitation probability exceedance curves (1950 to 1999)

Table 1 Final set of potential predictors used in the January downscaling model and their correlations withobserved precipitation in each time slice and whole period.

Rank of variable Potential variables for January Gridlocation

Time slice Correlationwith

precipitation

1 Surface precipitation rate 4,4

1950-1969 0.9101970-1989 0.5811990-2010 0.6511950-2010 0.693

2 1000hPa specific humidity 3,3

1950-1969 0.5321970-1989 0.5321990-2010 0.6031950-2010 0.550

3 850hPa meridional wind 3,6

1950-1969 -0.4661970-1989 -0.6981990-2010 -0.4681950-2010 -0.548

4 850hPa meridional wind 3,5

1950-1969 -0.4001970-1989 -0.7241990-2010 -0.5221950-2010 -0.544

5 1000hPa specific humidity 3,4

1950-1969 0.4871970-1989 0.5531990-2010 0.5161950-2010 0.515

6 850hPa meridional wind 2,6

1950-1969 -0.4201970-1989 -0.5851990-2010 -0.5061950-2010 -0.513

7 2m specific humidity 3,3

1950-1969 0.4301970-1989 0.5501990-2010 0.5401950-2010 0.510

8 Surface precipitation rate 3,3

1950-1969 0.6081970-1989 0.4131990-2010 0.5231950-2010 0.498

9 1000hPa specific humidity 4,4

1950-1969 0.5951970-1989 0.5081990-2010 0.4121950-2010 0.494

10 850hPa relative humidity 1,2

1950-1969 0.4381970-1989 0.4751990-2010 0.5961950-2010 0.483

11 2m specific humidity 3,4

1950-1969 0.4481970-1989 0.5331990-2010 0.4821950-2010 0.482

Table 2 Final sets of potential predictors for each calendar month

Month Potential variables used in the model with grid locationsJanuary Surface precipitation rate {(3,3),(4,4)}

1000hPa specific humidity {(3,3),(3,4),(4,4)}850hPa meridional wind {(2,6),(3,5),(3,6)}850hPa relative humidity {(1,2)}2m specific humidity {(3,3),(3,4)}

February Surface precipitation rate {(3,4),(4,4),(4,5)}

March Surface precipitation rate {(3,3),(3,4),(3,5),(4,3),(4,4),(4,5),(4,6)}

April 850hPa relative humidity {(4,3),(4,4)}Surface precipitation rate {(4,3)}

May Surface precipitation rate {(4,4),(5,5)}850hPa geopotential height {(4,3)}

June Surface precipitation rate {(3,2),(3,3),(4,2),(4,3),(4,4),(4,5)}Mean sea level pressure {(4,3),(5,3)}850hPa zonal wind {(2,4)}Surface pressure{(4,3),(5,3),(5,4)}

July 850hPa zonal wind {(1,3),(1,4)}850hPa geopotential height {(4,3),(4,4),(4,5)}

August Surface precipitation rate {(4,3),(5,4),(5,5)}

September Surface precipitation rate {(2,1),(2,2),(3,2),(3,3),(3,5),(4,2),(4,3),(4,4),(4,5)}850hPa relative humidity {(3,3)}700hPa relative humidity {(3,4)}

October Surface precipitation rate {(3,2),(4,2),(4,3),(4,4)}850hPa relative humidity {(4,3)}700hPa geopotential height {(1,1)}

November 850hPa relative humidity {(3,2),(3,3)}Surface precipitation rate {(4,3),(4,5)}

December Surface precipitation rate {(2,1),(3,2),(4,3),(4,4),(5,5)}850hPa relative humidity {(3,2)}

hPa = Atmospheric pressure in hectopascal; and the locations are given within brackets (see Figure 1)

Table 3 Performances of downscaling models in calibration and validation

Statistic

Calibration (1950-1989) Validation (1990-2010) /(1990-1999)*

Observations Model(NCEP/NCAR) Model(HadCM3)

ObservationsModel(NCEP/NCAR) Model(HadCM3)1990-

20101990-1999

Avg 81.8 82.0 81.7 73.3 81.8 81.0 87.6Std 61.7 53.2 41.1 56.9 64.3 51.9 44.5Cv 0.75 0.65 0.50 0.78 0.79 0.64 0.51NSE 0.74 0.44 0.70 0.17SANS 0.66 0.26 0.61 -0.20R2 0.74 0.44 0.72 0.22Avg = average of monthly precipitation in mm, Std = standard deviation of monthly precipitation in mm, Cv = coefficient ofvariation, SANS = Seasonally Adjusted Nash Sutcliffe efficiency, NSE = Nash Sutcliffe efficiency, R2 = coefficient ofdetermination, *Note: bold italicised values in the table refer to period 1990-1999.

Table 4 Seasonal performances of downscaling models

Model StatisticCalibration (1950-1989) Validation (1990-2010)/(1990-1999)*

Season SeasonSummer Autumn Winter Spring Summer Autumn Winter Spring

ObservedAvg

40.7 73.7 125.1 87.7 42.9/(44.3) 54.1/(57.0) 119.4/(136.1) 78.3/(89.8)Model(NCEP/NCAR) 40.7 73.7 125.1 87.7 49.2 57.8 132.5 85.1Model(HadCM3) 40.3 73.8 125.1 87.8 (44.9) (78.8) (128.3) (98.5)

ObservedStd

33.7 58.8 64.5 53.5 41.0/(46.8) 43.1/(46.5) 61.2/(66.3) 48.4/(55.1)Model(NCEP/NCAR) 26.0 46.6 54.1 43.9 29.8 33.1 54.1 41.7Model(HadCM3) 15.6 34.4 26.7 30.5 (12.7) (39.0) (30.0) (42.0)

ObservedCv

0.83 0.80 0.52 0.61 0.96/(1.06) 0.80/(0.82) 0.51/(0.49) 0.62/(0.61)Model(NCEP/NCAR) 0.64 0.63 0.43 0.50 0.61 0.57 0.41 0.49Model(HadCM3) 0.39 0.47 0.21 0.35 (0.28) (0.49) (0.23) (0.43)

Model(NCEP/NCAR) NSE0.60 0.63 0.70 0.67 0.42 0.75 0.58 0.64

Model(HadCM3) 0.16 0.34 0.17 0.33 (0.12) (-0.58) (-0.20) (-0.15)

Model(NCEP/NCAR) R2 0.60 0.63 0.70 0.67 0.45 0.71 0.63 0.65Model(HadCM3) 0.16 0.34 0.17 0.33 (0.13) (0.04) (0.00) (0.09)

Avg = average of monthly precipitation in mm, Std = standard deviation of monthly precipitation in mm, Cv = coefficient ofvariation, NSE = Nash Sutcliffe efficiency, R2 = coefficient of determination, *Note: bold italicised values in brackets in thetable refer to period 1990-1999.